A lattice model for condensation in Levin-Wen systems

Christian, Jessica; Green, David; Huston, Peter; Penneys, David

doi:10.1007/jhep09(2023)055

J. High Energ. Phys.

2023

DOI: 10.1007/jhep09(2023)055

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A lattice model for condensation in Levin-Wen systems

Jessica Christian,

David Green,

Peter Huston

et al.

Abstract: Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra… Show more

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Cited by 6 publications

References 49 publications

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Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Jia,

Tan,

Kaszlikowski

2024

J. High Energ. Phys.

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We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into their associated weak Hopf symmetries. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra, leading to a reducible vacuum string label; the charge symmetry, serving as a quantum double of gauge symmetry, constitutes a connected weak Hopf algebra. This implies that the associated topological phase retains its characterization by a unitary modular tensor category (UMTC). The bulk charge symmetry can also be captured by a weak Hopf tube algebra. We offer an explicit construction of the weak Hopf tube algebra structure and thoroughly discuss its properties. The gapped boundary and domain wall models are extensively discussed, with these 1d phases characterized by unitary multifusion categories (UMFCs). We delve into the gauge and charge symmetries of these 1d phases, as well as the construction of the boundary and domain wall tube algebras. Additionally, we illustrate that the domain wall tube algebra can be regarded as a cross product of two boundary tube algebras. As an application of our model, we elucidate how to interpret the defective string-net as a restricted multifusion string-net.

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Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Jia,

Tan,

Kaszlikowski

2024

J. High Energ. Phys.

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Levin-Wen is a Gauge Theory: Entanglement from Topology

Kawagoe,

Jones,

Sanford

et al. 2024

Commun. Math. Phys.

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We show that the Levin-Wen model of a unitary fusion category $${\mathcal {C}}$$ C is a gauge theory with gauge symmetry given by the tube algebra $${\text {Tube}}({\mathcal {C}})$$ Tube ( C ) . In particular, we define a model corresponding to a $${\text {Tube}}({\mathcal {C}})$$ Tube ( C ) symmetry protected topological phase, and we provide a gauging procedure which results in the corresponding Levin-Wen model. In the case $${\mathcal {C}}=\textsf{Hilb}(G,\omega )$$ C = Hilb ( G , ω ) , we show how our procedure reduces to the twisted gauging of a trival G-SPT to produce the Twisted Quantum Double. We further provide an example which is outside the bounds of the current literature, the trivial Fibbonacci SPT, whose gauge theory results in the doubled Fibonacci string-net. Our formalism has a natural topological interpretation with string diagrams living on a punctured sphere. We provide diagrams to supplement our mathematical proofs and to give the reader an intuitive understanding of the subject matter.

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Dynamical Abelian anyons with bound states and scattering states

Bachmann

Nachtergaele

Siddharth

2023

Journal of Mathematical Physics

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We introduce a family of quantum spin Hamiltonians on Z2 that can be regarded as perturbations of Kitaev’s Abelian quantum double models that preserve the gauge and duality symmetries of these models. We analyze in detail the sector with one electric charge and one magnetic flux and show that the spectrum in this sector consists of both bound states and scattering states of Abelian anyons. Concretely, we have defined a family of lattice models in which Abelian anyons arise naturally as finite-size quasi-particles with non-trivial dynamics that consist of a charge-flux pair. In particular, the anyons exhibit a non-trivial holonomy with a quantized phase, consistent with the gauge and duality symmetries of the Hamiltonian.

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A lattice model for condensation in Levin-Wen systems

Cited by 6 publications

References 49 publications

Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Levin-Wen is a Gauge Theory: Entanglement from Topology

Dynamical Abelian anyons with bound states and scattering states

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